# Question: a The mean of a random sample of 25 observations

a. The mean of a random sample of 25 observations from a normal population with a standard deviation of 50 is 200. Estimate the population mean with 95% confidence.

b. Repeat part (a) changing the population standard deviation to 25.

c. Repeat part (a) changing the population standard deviation to 10.

d. Describe what happens to the confidence interval estimate when the standard deviation is decreased.

b. Repeat part (a) changing the population standard deviation to 25.

c. Repeat part (a) changing the population standard deviation to 10.

d. Describe what happens to the confidence interval estimate when the standard deviation is decreased.

**View Solution:**## Answer to relevant Questions

a. A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine the 95% confidence interval estimate of the population mean.b. Repeat part (a) with a sample size ...a. A random sample of 100 observations was randomly drawn from a population with a standard deviation of 5. The sample mean was calculated as x̄ = 400. Estimate the population mean with 99% confidence.b. Repeat part (a) ...H0: µ = 15H1: µ < 15σ = 2, n = 25, x̄ = 14.3, α = .10Calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution.Determine β for the following test of hypothesis, given that µ = 48.H0: µ = 50H1: µ < 50α = .05, σ = 10, n = 40Draw the operating characteristic curve for n = 10, 50, and 100 for the following test:H0: µ = 400H1: µ > 400α = .05, σ = 50Post your question